Variations of local heat transfer coefficient in piped flow of viscous liquids

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

Investigating viscous fluid flow in an internal mixer using computational fluid dynamics

This thesis presents an effective methodology for the generation of a simulation which can be used to increase the understanding of viscous fluid processing equipment and aid in their development, design and optimisation. The Hampden RAPRA Torque Rheometer internal batch twin rotor mixer has been simulated with a view to establishing model accuracies, limitations, practicalities and uses. As this research progressed, via the analyses several 'snap-shot' analysis of several rotor configurations using the commercial code Polyflow, it was evident that the model was of some worth and its predictions are in good agreement with the validation experiments, however, several major restrictions were identified. These included poor element form, high man-hour requirements for the construction of each geometry and the absence of the transient term in these models. All, or at least some, of these limitations apply to the numerous attempts to model internal mixes by other researchers and it was clear that there was no generally accepted methodology to provide a practical three-dimensional model which has been adequately validated. This research, unlike others, presents a full complex three-dimensional, transient, non-isothermal, generalised non-Newtonian simulation with wall slip which overcomes these limitations using unmatched ridding and sliding mesh technology adapted from CFX codes. This method yields good element form and, since only one geometry has to be constructed to represent the entire rotor cycle, is extremely beneficial for detailed flow field analysis when used in conjunction with user defined programmes and automatic geometry parameterisation (AGP), and improves accuracy for investigating equipment design and operation conditions. Model validation has been identified as an area which has been neglected by other researchers in this field, especially for time dependent geometries, and has been rigorously pursued in terms of qualitative and quantitative velocity vector analysis of the isothermal, full fill mixing of generalised non-Newtonian fluids, as well as torque comparison, with a relatively high degree of success. This indicates that CFD models of this type can be accurate and perhaps have not been validated to this extent previously because of the inherent difficulties arising from most real processes.

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

Hydrodynamics and mass transfer studies in a scheibel extractor

A 10 cm diameter four-stage Scheibel column with dispersed phase wetted packing sections has been constructed to study the hydrodynamics and mass transfer using the system toluene-acetone-water. The literature pertaining to the above extractor has been examined and the important phenomena such as droplet break-up and coalescence, mass transfer and backmixing have been reviewed. A critical analysis of the backmixing or axial mixing models and the corresponding techniques for parameter estimation was applied and an optimization technique based on Marquardt's algorithm was implemented. A single phase sampling technique was developed to estimate the acetone concentration profile in both phases along the column. Column flooding characteristics were investigated under various operating conditions and it was found that, when the impellers were located at about DI/5cm from the upper surface of the pads, the limiting flow rates increased with impeller speed. This unusual behaviour was explained in terms of the pumping effect created by the turbine impellers. Correlations were developed to predict Sauter mean drop diameters. A five-cell with backflow model was used to estimate the column performance (stage efficiency) and phases non-ideality (backflow parameters). Overall mass transfer coefficients were computed using the above model and compared with those calculated using the correlations based on single drop mechanism.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Comparative analysis of experimental and modelling of gas-solid flow hydrodynamics:effect of friction and interparticle cohesion forces

The effect of friction and interparticle cohesion forces on the gas-solid flow hydrodynamics was discussed. A proposed interparticle cohesion and frictional force terms have been tested in a continuum fully developed flow model to investigate their effect on the general hydrodynamic features of vertical duct flow. It was observed that both terms have direct effect on lowering the material carryover, which implies a reduced bed expansion in freely bubbling column. The parametric analysis shows that cohesion and frictional forces are high when compared to kinetic stress and hence it can play a major role in describing the hydrodynamics features of the flow.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

Visualising and controlling the flow in biomolecular systems at and between multiple scales:from atoms to hydrodynamics at different locations in time and space

A novel framework for modelling biomolecular systems at multiple scales in space and time simultaneously is described. The atomistic molecular dynamics representation is smoothly connected with a statistical continuum hydrodynamics description. The system behaves correctly at the limits of pure molecular dynamics (hydrodynamics) and at the intermediate regimes when the atoms move partly as atomistic particles, and at the same time follow the hydrodynamic flows. The corresponding contributions are controlled by a parameter, which is defined as an arbitrary function of space and time, thus, allowing an effective separation of the atomistic 'core' and continuum 'environment'. To fill the scale gap between the atomistic and the continuum representations our special purpose computer for molecular dynamics, MDGRAPE-4, as well as GPU-based computing were used for developing the framework. These hardware developments also include interactive molecular dynamics simulations that allow intervention of the modelling through force-feedback devices.

Multiscale molecular dynamics/hydrodynamics implementation of two dimensional “Mercedes Benz” water model

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.

Dynamic analysis of submerged microscale plates:the effects of acoustic radiation and viscous dissipation

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate- fluid interaction problem is developed on the basis of linearized Navier-Stokes equations and noslip conditions. Analytical expression for the fluidloading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers beingmass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.